Hierarchical Storage System With The Matrix Eigenvalue High-performance Computing Research

Because of the speed gap between fast processor and relatively slow memory, memory access is always a bottleneck of the computer systems for many types of computations. In order to solve this serious problem, hierarchical memory structure is widely used in modern computer systems. Cache memories help bridge the cycle time gap between central processors and main memories. Thus, cache has been a key component to the computation speed.Eigenvalue problem is one of the basic problems in scientific and engineering computations. Various algorithms are used to solve this problem, such as the power and anti-power method, subspace iteration method, QR method, Jacobi method, and so on. Researchers revised these algorithms with various skills, which efficiently improve their performance in practical computation. In the meantime, searching for new methods may lead to brand new clues of high performance computation of eigenproblem. Eigenproblem is widely used in various applications, so its efficiency has important effects on high performance computation of computer systems.The computation performance of applications on a hierarchical memory depends mainly on the performance of cache-memory level, which is in turn dependent on the efficient use of program locality. There are three aspects that affect the cache utilization rate: the access mode of data, the data allocation mode in memory and the organization of cache. Accordingly, we can change the data access mode, alter data allocation mode and improve the organization of cache, all of which can enlarge the utilization rate of cache.Even if there is much locality in programs, the improper data organization may still bring data access conflicts in...